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Simplifying 153 = x(7 + x) 153 = (7 * x + x * x) 153 = (7x + x2) Solving 153 = 7x + x2 Solving for variable 'x'. Reorder the terms: 153 + -7x + -1x2 = 7x + -7x + x2 + -1x2 Combine like terms: 7x + -7x = 0 153 + -7x + -1x2 = 0 + x2 + -1x2 153 + -7x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 153 + -7x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -153 + 7x + x2 = 0 Move the constant term to the right: Add '153' to each side of the equation. -153 + 7x + 153 + x2 = 0 + 153 Reorder the terms: -153 + 153 + 7x + x2 = 0 + 153 Combine like terms: -153 + 153 = 0 0 + 7x + x2 = 0 + 153 7x + x2 = 0 + 153 Combine like terms: 0 + 153 = 153 7x + x2 = 153 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = 153 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 153 + 12.25 Combine like terms: 153 + 12.25 = 165.25 12.25 + 7x + x2 = 165.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 165.25 Calculate the square root of the right side: 12.854960132 Break this problem into two subproblems by setting (x + 3.5) equal to 12.854960132 and -12.854960132.Subproblem 1
x + 3.5 = 12.854960132 Simplifying x + 3.5 = 12.854960132 Reorder the terms: 3.5 + x = 12.854960132 Solving 3.5 + x = 12.854960132 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 12.854960132 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 12.854960132 + -3.5 x = 12.854960132 + -3.5 Combine like terms: 12.854960132 + -3.5 = 9.354960132 x = 9.354960132 Simplifying x = 9.354960132Subproblem 2
x + 3.5 = -12.854960132 Simplifying x + 3.5 = -12.854960132 Reorder the terms: 3.5 + x = -12.854960132 Solving 3.5 + x = -12.854960132 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -12.854960132 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -12.854960132 + -3.5 x = -12.854960132 + -3.5 Combine like terms: -12.854960132 + -3.5 = -16.354960132 x = -16.354960132 Simplifying x = -16.354960132Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.354960132, -16.354960132}
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